If we take the most basic reading of Nietzsche's ideas of "God is Dead," one can see how Pope Pius IX would clearly define it as an error based on his own logic in the "Syllabus." Consider the Nietzschean notion of the death of God in his own words:

God is dead. God remains dead. And we have killed him. Yet his shadow still looms. How shall we comfort ourselves, the murderers of all murderers? What was holiest and mightiest of all that the world has yet owned has bled to death under our knives: who will wipe this blood off us? What water is there for us to clean ourselves? What festivals of atonement, what sacred games shall we have to invent? Is not the greatness of this deed too great for us? Must we ourselves not become gods simply to appear worthy of it?

Nietzsche's words help to establish some basic ideas. The first is that the role of the "supernatural" is absent in modern thought. Nietzsche makes it clear that human beings have removed everything but the shadow of the divine and in the process have assented to this role. At the same time, it becomes clear that a world in which the supernatural is not merely absent but also one in which the human being has become their own force of supernatural is indicative of the modern condition. For Pope Pius IX, this becomes the basis of indictment in his "Syllabus of Errors." Initially, Pope Pius IX argues that modern philosophy is wrong when it fails to account for the supernatural and the divine. Nietzsche does not account for this, and thus his views could be seen as modern and incorrect in such a logic. At the same time, Pope Pius' assertions sought to attack the sweeping "away [of] the foundations of all human and Divine order." Nietzsche would be considered "modern" in this light with his assertion regarding the basic idea of where the divine has gone. It is here in which Pope Pius' "Syllabus of Errors" would find Nietzsche to be both modern and incorrect in his beliefs.